Simplify the following expression: $x = \dfrac{-80k + 40}{72k}$ You can assume $k \neq 0$.
Solution: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-80k + 40 = - (2\cdot2\cdot2\cdot2\cdot5 \cdot k) + (2\cdot2\cdot2\cdot5)$ The denominator can be factored: $72k = (2\cdot2\cdot2\cdot3\cdot3 \cdot k)$ The greatest common factor of all the terms is $8$ Factoring out $8$ gives us: $x = \dfrac{(8)(-10k + 5)}{(8)(9k)}$ Dividing both the numerator and denominator by $8$ gives: $x = \dfrac{-10k + 5}{9k}$